The finite, the infinite and the inexhaustibility of matter

Dialectical materialism affirms the inexhaustible nature of matter. The universe is only material, and it is infinite. This means that there is no space or time without matter, that matter is everywhere and always present. Whether we look to the infinitely small or the infinitely large, whether we look to the past, the present or the future, we will always have matter and only matter.

This aspect of matter is dialectically opposed to another aspect: that of its continuity. Dialectical materialism asserts that matter forms a whole, a whole in which everything is interrelated. At no point can we find a thing or phenomenon that is indivisible, isolated, irreducibly independent of the rest.

The dialectical paradox of the universe

There’s a dialectical paradox here. On the one hand, the universe is made up of an infinite number of different, and therefore distinguishable, things. On the other, the universe is absolutely continuous, undivided, all part of a single, infinitely rich, yet unified reality.

On the one hand, there is only one determination, that of the universe forming a whole where everything is interrelated, where nothing exists without being related to everything else.

On the other hand, there is an infinity of determinate things, each thing, each phenomenon possessing its own unity and consequently its own identity arising from its own difference from the rest.

However, dialectically, an infinity of determinate things posits an indeterminate infinity, since the identities of its elements are infinite.

On the one hand, then, we have a universe that is determined, because it is unified, uni-total… and, at the same time, a universe whose infinite nature is lost, in terms of definitions, in the infinity of what exists. The resolution of this question is complex.

The attempt at a religious answer
through the one and the many

What dialectical materialism understands as the opposition between the finite and the infinite has in the past been understood as the opposition between the one and the many. This is at the heart of the thinking of what is called philosophy.

The traditional starting point for this is philosophical questioning in Greece before Plato and Aristotle, with two philosophers highlighted here. There’s Parmenides, who says that the universe is one, always the same, and that consequently once we’ve talked about it, we can not speak more, since everything has already been said.

Then there’s Heraclitus, for whom everything is always changing: you can’t bathe in the same river twice. Consequently, we need to speak uninterruptedly, in order to always define things that are in essence always changing.

In one case, the universe is unity, in the other it is multiplicity. The notion of God was formulated intellectually precisely to be able to interpret this relationship between the one and the many.

For Plato, the material world is nothing but an illusion, a pale reflection of the only true reality, which is spiritual and is God. This is the message of the allegory of the cave. For Aristotle, on the other hand, the material world has all its dignity, with God serving merely as a “motionless motor” to set material things in motion in a continuous interplay of cause and effect.

Naturally, religions, which by definition necessarily follow Plato, have had great difficulty in justifying how the divine “one” can give rise to the material “many” (in some cases, the finite “emanates” from the infinite by degrees, other explanations invent an intermediary God playing the role of demiurge, others multiply the intermediate stages between the two or, on the contrary, make God “recede”, etc.).

In all cases, however, a relationship is established between the one and the many, making it possible to grasp the many by means of the concept of “one” (divine), and to establish definitions and determinations.

Religions are precisely those ethical, social, psychological, political, economic and other determinations. It is necessary to submit to the definitions laid down by the “one” (divine), which is the origin of the “many”. In any case, at the end of time, the multiple must give way to the “one”.

The bourgeois attempt at an empirio-critical response

In reality, God has only a conceptual reality, allowing us to posit the relationship between the finite and the infinite in one way or another. Moreover, according to its historical needs, humanity has modulated the relationship between God and the world, the one and the many. Protestantism, by affirming the unity of personal consciousness, thus reformulates the relationship to God in its entirety.

Religious formalism was, and still is, less tenable in the face of the observation of movement, whether in the past with the history of the planet, the history of species, or in the present, with expanding human activities.

As the productive forces grew, religions saw their concept weaken, allowing science to assert itself in human activities.

However, under the weight of bourgeois domination, science has been increasingly reduced to utilitarian pragmatism.

Its vision of the world is summed up in a more or less critical empiricism, combined with a wholly idealistic positivism, a genuine belief in “progress” consisting in the simple accumulation of data.

There would be a linear development of the sciences, as techniques and functional capacities would become more widespread.

In reality, it’s not so much a question of science as of a technical upsurge driven by the development of productive forces.

Under the bourgeoisie, scientists have even become so freewheeling that they can no longer even fight the idea of God, getting bogged down in a blissful cult of experimentation and a relativism presented as materialism.

The dialectical materialist response through cosmology

Dialectical materialism rejects both the religious interpretation of a relationship between the one and the many, and the more or less critical empiricism of a science reduced to techniques and experimentation.

Dialectical materialism posits the universe – i.e., matter – as the basis of any authentically scientific perspective. In so doing, it resolves the problem of the relationship between the elements of the universe and the universe itself.

It is because there is, dialectically, the infinite in the finite and the finite in the infinite, that it is possible to grasp how the universe is a single entity which, at the same time, possesses an infinite nature.

There is no such thing as a definite quantity of matter, which is static and simply “formed” from the outside. Only matter exists, and matter is self-moving. There is no external impulse to matter.

Nor is there any pause in the incessant movement of matter: there is never a halt in the process of matter’s transformation.

The universe is composed solely of matter, and this matter is in uninterrupted transformation, experiencing dialectical leaps based on the internal contradictions inherent in each thing, each phenomenon.

Since matter knows no external impulse or origin, and yet exists, then it has always existed, and always will. Since matter knows dialectical jumps, then it has always existed by knowing these dialectical jumps, and it exists by knowing these dialectical jumps, everywhere and all the time.

Since dialectical leaps take place everywhere and all the time, there is no limit to matter or its development.

The question of the relationship between whole and parts

How do incessant dialectical leaps relate to the unified, uni-total character of the universe? The basic problem is that what is infinite is logically incapable of having parts.

If infinity had parts, they would be finite or infinite. If these parts are infinite, then there would be several infinities, which is not coherent. If the parts are finite, then the infinite would be made up of finite elements, and could not be infinite.

One solution would be to conceive of an infinity of finite parts, which was Spinoza’s solution for expressing the inexhaustible character of the “modes” of existence of the entirely material universe. Here, the universe would be infinite in the sense that it would consist of an infinity of modes that themselves exist infinitely. All modes would be related in their very existence, as they would be of the “nature naturated” by the whole, which is “naturating nature”.

To define a thing or a phenomenon, we must therefore not have a positive reading, starting from “nothing” to get to the thing, but extract the thing from the whole: for Spinoza, “all definition is negation” (in the sense that a thing is not everything else).

However, this is not to posit a qualitative infinity, but to affirm that there is a dimension measurable to infinity, even if this measurement never ceases, quantitatively, going precisely to infinity.

Spinoza’s quantitatively infinite universe, with its concept of negation as the definition of everything, nevertheless paved the way for dialectics.

Negation as determination

It was Hegel who posited infinity as a qualitative leap from the finite. Unfortunately, he saw the movement of the world as passing through the human mind’s grasp of dialectics, rather than through the dialectical transformation of the world itself.

Hegel’s extension of Spinoza (who in turn extended Aristotle, Avicenna and Averroës) nevertheless posited transformation as the key to understanding phenomena.

Dialectical materialism does not consider the finite and the infinite to be separate. There is no irreducible “one” and “many” facing each other. In reality, God has only been the mask for the concept of infinity, and the term multiple has only designated the finite.

And yet, according to the law of contradiction, the finite is infinite and the infinite finite. Hegel understood this based on Spinoza’s definition of negation.

He understood that if a thing defines itself negatively (in the sense that a thing is not something else), then it must also be defined negatively in relation to itself.

Difference then becomes a thing’s identity. Every thing is both itself (because it is not something else) and other than itself, because it carries its own finitude.

Hegel, in The Science of Logic, notes that: “Difference as such is already contradiction in itself; it is in fact the unity of things that are only insofar as they are not one – and the separation of things that are only insofar as they are separated in the same relation.

The positive and the negative, on the other hand, are the contradiction posited, because as negative units they pose themselves, and hence the overcoming of the latter and the positing of its opposite.”

The direct consequence of considering that a thing, a phenomenon, poses itself as difference, is that there is a dialectical identity. This means that in its very existence, every thing posits itself as finite in the infinite, because it differs from the infinity of things. It posits itself as different, and therefore allows itself to be determined by this difference, by this negation of the rest.

Lenin, in his notes on this work by Hegel, makes the following remark on this question:

“[Hegel:] “They” (things) “are, but the truth of this being is their end.”

Shrewd and clever! Hegel analyses concepts that usually appear to be dead and shows that there is movement in them.

Finite? That means moving to an end!

Something?—means not that which is Other.

Being in general?— means such indeterminateness that Being = not-Being. All-sided, universal flexibility of concepts, a flexibility reaching to the identity of opposites,—that is the essence of the matter.

This flexibility, applied subjectively = eclecticism and sophistry.

Flexibility, applied objectively, i.e. reflecting the all-sidedness of the material process and its unity, is dialectics, is the correct reflection of the eternal development of the world.”

The dialectic of finite and infinite

It is from this contradictory relationship between the finite and the infinite that we must understand the inexhaustible nature of matter. Each thing is inherently different, and thus already the basis of a dialectical opposition. What’s more, in its very nature of being finite, it will cease to exist. It therefore carries an internal contradiction: it is, but it also contains its own death.

And this is universal. This means that finitude is infinite. And since, what’s more, everything transforms itself, this means that everything carries the infinite, since what is finite yields to transformation, in a qualitative leap, opening the way to something new, a non-finite within the finite, and thus the infinite.

In his notes, Lenin transcribes the following lines from Hegel:

“The unity of finite and infinite is not an external juxtaposition of these terms, nor an improper connection contrary to their determination, and binding together entities separate and opposed and mutually independent and hence incompatible.

On the contrary, each in itself is this unity, and is so only in transcending itself, neither excelling the other in Being-in-Self and affirmative Existent Being.

It has been demonstrated above that finitude exists only as a passing beyond itself; it thus contains infinity, which is its Other.…”

Lenin writes the following remark next to this quote:

« To be applied to atoms versus electrons. In general the infiniteness of matter deep within…”

Lenin prefigures here, as Mao Zedong did, the non-indivisible character of matter as regards atoms and their components. However, this is true not only in depth, but in all directions.

Infinity, non-infinity, continuity, discontinuity

We need to distinguish between infinity and non-infinity. A thing experiencing a qualitative leap is a finite thing carrying non-finiteness within it, as the new emerges from the old. We could say that, in the qualitative leap, a thing demolishes the limits apparently assigned to it.

Hegel, in The Science of Logic, sums this up by saying that: “It is the nature of the finite itself to surpass itself, to negate its negation, and to become infinite.”

The non-finite extracts itself from the finite. However, the question of the infinite still arises. Hegel has failed to define it here, because he has turned it into an abstract principle that overhangs reality. For him, infinity is the meaning of development, and therefore of the world, and the world no longer counts for him.

Dialectical materialism considers that it is the world which carries movement, development and therefore infinity. This means that infinity is by definition present in matter, as Lenin observed with “the infinity of matter in depth”.

In fact, one of the essential aspects of the process and the most disturbing for a human observer is that the infinite nature of matter combines with its opposite, its finite nature.

However, it is here in relation to the contradiction between continuity and discontinuity. Every phenomenon carries contradiction within itself, and therefore difference, because every contradiction affirms a phenomenon and consequently separates itself from the rest of matter to take on a finite, different character.

This poses a discontinuity in the infinite character of matter, but at the same time this discontinuity implies continuity, nothing being isolated.

An object made by a human being is, for example, inseparable from the productive forces carried by humanity, just as a cloud is inseparable from the general terrestrial system, the Biosphere.

However, if the productive forces of humanity cannot be explained without the terrestrial Biosphere, it cannot be explained without the galaxy, which itself depends on a super-cluster of galaxies, etc.

All this is true for the infinitely large and the infinitely small, to infinity.

There is no “final” level, whether towards the infinitely large or the infinitely small – otherwise, this “final” level would be isolated, independent, even a framework.

The infinitely large and the infinitely small themselves form a contradiction. There is thus both continuity and discontinuity in existence. A thing is both in continuity with the rest of the universe… And, through its internal contradiction, has its own leap.

The universe and its constitution in waves

The universe is a sort of infinite ocean made up of infinite waves responding to each other, transforming each other, to infinity.

Matter transforms matter, deepens it, develops it, and this does the same, to infinity.

The existence in the sense of elements relatively separated from the general movement of the universe is based on the waves of qualitative leaps occurring in matter itself. This in no way means that the contradiction of each thing is not internal, but that its framework relates to matter as a whole. To take an example, the Earth is the product of a qualitative leap in the organization of matter at the galaxy level, and one of the waves produced by the existence of the Earth is the formation of humanity, which itself forms a wave having an impact on its direct spatial environment, etc.

Every echo is infinite

Every qualitative leap has an infinite echo, because however small this echo may be, it is part of the general movement of matter.

Every finite thus carries within itself not only the non-finite of its own leap, of its own transformation, but also the infinite itself due to the fact that it relates to a general movement of matter.

It is not at all a question here of the existence of a simple “limit” pushed back from an expanding finite, but of infinity in the strict sense, that is to say non-measurable and non-divisible.

The slightest material element taken arbitrarily possesses in itself infinity, the infinite extension of matter, since it is part of it. Matter is infinite in its reality and the partial possesses the totality, the finite the infinite, and vice versa. In no case is it possible to speak of “parts” of matter.

If they were parts, then they would have to be given a special status. Their identity would each be opposed to the other parts, and therefore relatively isolated. However, no isolation is possible in the infinite nature of matter, because infinity cannot be finite.

Consequently, the separations that exist within material infinity, i.e. the existence of finite elements within infinity, must be defined as a moment, a stage, a relative situation, proper to the expansion, growth and thickening of matter. They are an aspect of infinity as the eternal movement of matter.

It is this aspect that mathematics observes, fixing and separating arbitrarily, for a momentary photograph of what in reality is in uninterrupted and infinite transformation.

Eternity and the inexhaustible nature of matter

What is finite has as its foundation the qualitative leap proper to the dialectic of the finite and the infinite, for the finite is the product of an infinite expressed in the finite.

The finite thus carries within it its own limit, which produces a leap to infinity; this leap leads to a finite situation which itself carries its limit, which itself produces a leap to infinity, and this to infinity, and therefore eternally.

What exists materially as a relatively autonomous entity – a human being, a tree, a table – has as its foundation the qualitative leap to infinity, and thus the contradiction between finite and infinite.

In this way, eternity is based on the uninterrupted and, so to say, the expanding presence of matter. This is not a mere spatial expansion. It is an extension in the sense of a qualitative movement progressing in an infinity of aspects.

In concrete terms, the contradictory movement of matter results in the production of an infinite number of contradictions, which themselves have an echo in matter. The law of contradiction is universal and it extends eternally through infinity, producing waves with an ever-greater impact in the universe.

The inexhaustible nature of matter

In a certain sense, we can say that matter is not only infinite, but that it goes on to infinity. Its movement of complexification is based on the infinite (as an internal leap resulting from the rupture within the finite) and goes towards infinity.

Matter is both infinite and in the process of becoming infinite – it’s a contradiction.

Dialectical materialism thus affirms the infinite character of matter, both in its finite existence and in its infinite nature. However, this infinite character relates to the infinity carried by the movement of matter in its universality, as its principal aspect. The infinite character of an ‘isolated’ material reality is solely an abstraction freezing the general movement of matter and its qualitative leaps producing cosmic waves consisting of transformations.

The waves in the universe, of the universe, are produced by different contradictions. This means that they are both finite, because they consist of a phenomenon that responds to an internal contradiction, and at the same time infinite, because their number is infinite, because they are part of the general movement of the universe, because their qualitative impact is itself infinite in the future, their source itself being infinite in the past.

The movement of matter, producing a qualitative leap in one phenomenon, which itself acts on other phenomena, other leaps, is therefore characterized by an uneven development, underlining both the identity and the difference of the leaps and the phenomena.

Any isolation of a thing is therefore necessarily arbitrary, at whatever level. And there is no such thing as a fixed matrix in the movement of matter. This is an essential aspect of movement, of the nature of matter, of the inexhaustible nature of matter. There is no fixed determination, because there are no separate, fixed ‘parts’ of matter.

Any focus on a particular aspect is simply a mathematical photograph of a given moment that has its dignity, but lets the internally-carried limit escape, and therefore the break that leads to the leap to infinity.

Matter is therefore inexhaustible, because its dialectical richness is infinite and carries infinity. To have a ‘stock’ of matter, we would need a ‘beginning’ – but this is impossible, because matter by definition carries infinity.

The realization of the law of contradiction

The contradiction between the finite nature of a thing, in the sense of its internal determination, and its finite expression in the world, produces in itself an internal tear, causing the infinite to re-express itself, to reassert itself. This is the law of contradiction: each thing, in existing, uninterruptedly affirms its difference, and thus posits negation.

This is true everywhere and all the time, ad infinitum. It is a consequence of the inexhaustible nature of matter.

The point here is not to confuse what is absolute with what is relative. It is not the finite form that is relative, but the infinite. In fact, the finite form itself carries the contradiction, and it is the contradiction that is universal. The development of the infinite is relative because it expresses contradiction.

Dialectical materialism is the science of the unity of opposites, not the religion of an abstract infinity.

However, the relative and the absolute also form a contradiction. The development of the infinite always prevails, because it is inherent in matter. For this reason, what is finite is only relative and is bound to disappear.

This is why every material entity is obliged to transform itself and can never be eternal. Nothing is eternal, everything is transformed, because only the whole exists, as a whole, but consequently also as an infinite whole, and therefore infinity in extension, expansion and deepening.

The eternity of a finite thing would be the cessation of movement, and therefore of infinity. Consequently, there would be no more movement, and there would never even have been any. Movement does not exist if there is no infinity.

The question is therefore whether the main aspect is infinity, motion or matter. Primitive materialism considers that it is matter, while materialism that recognizes the dynamics of matter chooses movement. Dialectical materialism considers that it is infinity, because matter implies movement, and therefore infinity.

However, dialectically, it is matter that carries infinity. The affirmation of dialectics thus establishes materialism. Dialectical materialism rests on the contradiction between matter and its own finitude, hence infinity, hence dialectic. This is the main aspect.

The infinity of matter

Dialectical materialism does not, therefore, make a fetish of matter in finite form, but celebrates the infinite as the most authentic reality of matter – and at the same time recognizes the full dignity of matter as the only reality, the bearer of the infinite. The universe is not composed of matter: it is matter. What we call the universe is matter in its infinite reality, whose waves propagate its general and particular transformations, in an infinite movement that produces the finite, itself both the carrier and the vector of the infinite.

This is why only dialectical materialism recognizes the dignity of reality. Only dialectical materialism can see the infinite in the finite, and therefore accord fundamental value to the finite. Far from losing itself in the infinite by affirming it, it is enthusiastic about reality and its movement, its transformation.

It is in transforming reality that inexhaustible matter is affirmed, forming the true meaning of life. Dialectical materialism sees movement as transformation (and not as dynamics), and assumes matter as a cosmic, infinite and therefore eternal reality.

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